He II Heat Transfer Through Random Packed Spheres

Superfluid helium (He II) contained in porous media is examined. In particular, heat transfer experiments were performed on He II contained in random packs of uniform size polyethylene spheres. Measured results include the steady state temperature and pressure drops across packs of spheres (35 micron, 49 micron, and 98 micron diameter) and the associated steady, step, and pulse heat inputs. Bath temperatures range from 1.6 K to 2.1 K to help grasp the superfluid effects. Laminar, turbulent, and transitional fluid flow regimes are examined. Turbulent results are fitted to an empirically derived turbulent He II heat flow in a channel equation with an added tortuosity (extra length traveled) term that accounts for the porous media. An average tortuosity of 1.33 ± 0.07 was obtained, which is in good agreement with the values of 1.36 - 1.41 concluded from published work on classical fluid pressure drop across random packed spheres. Laminar permeability and shape factor results are compared to past studies of He II in porous media and in channel flows. The average critical heat flux, which describes the onset of turbulence, is predicted to be 0.19 W cm-2. The onset of turbulence is determined through a critical heat flux from which a critical Reynolds number is formulated, but does not describe He II turbulence in the normal fluid component. Other proposed He II "Reynolds numbers" are examined. The addition of the laminar and turbulent heat flow equations into a unifying prediction fits the transition regime data within 25 %. Transient temperatures compare favorably to a one-dimensional numerical solution that considers a variable Gorter-Mellink exponent and a piece-wise determination of the heat flux. Turbulent pressure drop results are fitted with empirically derived friction factors. The laminar permeability and equivalent channel shape factor derived from the pressure drop are compared the permeability and shape factor obtained from the temperature drop. Results from the pressure drop experiments are more accurate than temperature drop experiments due to reduced measurement errors with the pressure transducer. Turbulent theories considering only dynamic pressure losses in the normal fluid yield the most consistent friction factors. The addition of the laminar and turbulent heat flow equations into a unifying prediction fits all regimes to within 10 %.